On Similarity and Reducing Subspaces of the -Shift plus Certain Weighted Volterra OperatorReport as inadecuate




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Journal of Function Spaces - Volume 2017 2017, Article ID 8370139, 8 pages - https:-doi.org-10.1155-2017-8370139

Research ArticleDepartment of Mathematics, Hebei Normal University, Hebei Province Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, China

Correspondence should be addressed to Yucheng Li

Received 15 February 2017; Accepted 30 March 2017; Published 13 April 2017

Academic Editor: Young Joo Lee

Copyright © 2017 Yucheng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be an -degree polynomial . Inspired by Sarason’s result, we introduce the operator defined by the multiplication operator plus the weighted Volterra operator on the Bergman space. We show that the operator is similar to on some Hilbert space . Then for , by using matrix manipulations, the reducing subspaces of the corresponding operator on the Bergman space are characterized.





Author: Yucheng Li, Hao Chen, and Wenhua Lan

Source: https://www.hindawi.com/



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